Logistic Regression

Gene filtering:

• Remove genes without cluster (Module=gray)

• Remove genes with Module-Trait correlation missing

rm_cluster = dataset[is.na(dataset$MTcor),clustering_selected] %>% unique %>% as.character

print(paste0('Removing ', sum(dataset[,clustering_selected]=='gray'), ' genes without cluster'))

## [1] "Removing 178 genes without cluster"

print(paste0('Removing ', sum(is.na(dataset$MTcor)), ' genes belonging to module(s) without module-trait correlation: ',
             rm_cluster))

## [1] "Removing 1555 genes belonging to module(s) without module-trait correlation: #00BD64"

new_dataset = dataset %>% filter(dataset[,clustering_selected]!='gray' & !is.na(MTcor))

Variable changes:

• Using Module Membership variables instead of binary module membership

• Not including p-value variables

• Including a new variable with the absolute value of GS

• Removing information from gray module (unclassified genes) and any other module that did not have a Module-Trait value

• Objective variable: Binary label indicating if it’s in the SFARI dataset or not (including score 6)

new_dataset = new_dataset %>% dplyr::select(-c(matches(paste('pval', clustering_selected,
                                               gsub('#','',rm_cluster), sep='|')), MMgray)) %>%
              mutate('absGS'=abs(GS), 'SFARI'=ifelse(gene.score=='None', FALSE, TRUE)) %>%
              dplyr::select(-gene.score)

rownames(new_dataset) = rownames(dataset)[!is.na(dataset$MTcor) & dataset[,clustering_selected]!='gray']

rm(rm_cluster)

original_dataset = dataset
dataset = new_dataset
print(paste0('The final dataset contains ', nrow(dataset), ' observations and ', ncol(dataset), ' variables.'))

## [1] "The final dataset contains 14867 observations and 38 variables."

rm(new_dataset)

Sample of the dataset

dataset %>% head %>% kable

Objective variable distribution: Unbalanced labels

print(table(dataset$SFARI))

## 
## FALSE  TRUE 
## 14039   828

cat(paste0('\n',round(mean(dataset$SFARI)*100,2), '% of the observations are positive'))

## 
## 5.57% of the observations are positive

Visualising the variables

Chose the t-SNE algorithm because it preserves distances

The SFARI labels is still close to the absolute value of Gene Significance. This time the MM variables seem to be grouped in 2 clusters

tsne = dataset %>% t %>% Rtsne(perplexity=10)

plot_data = data.frame('ID'=colnames(dataset), 'C1'=tsne$Y[,1], 'C2'=tsne$Y[,2],
                       type=ifelse(grepl('MM', colnames(dataset)),'ModMembership',
                            ifelse(grepl('SFARI', colnames(dataset)), 'SFARI',
                            ifelse(grepl('GS', colnames(dataset)), 'GS', 'MTcor'))))

ggplotly(plot_data %>% ggplot(aes(C1, C2, color=type)) + geom_point(aes(id=ID)) + 
         theme_minimal() + ggtitle('t-SNE visualisation of variables'))

The Module Membership variables are grouped by Module-Trait correlation, with positive correlations on one side, negative on the other, and modules with low correlation far away from the SFARI tag

mtcor_by_module = original_dataset %>% dplyr::select(matches(clustering_selected), MTcor) %>% unique
colnames(mtcor_by_module) = c('ID','MTcor')

plot_data = mtcor_by_module %>% mutate(ID = gsub('#','MM.',ID)) %>% right_join(plot_data, by='ID')

ggplotly(plot_data %>% ggplot(aes(C1, C2, color=MTcor)) + geom_point(aes(id=ID)) + 
         scale_color_viridis() + theme_minimal() + 
         ggtitle('t-SNE of variables coloured by Module-Diagnosis correlation'))

rm(mtcor_by_module, tsne)

Visualising the observations

# Mean Expression data
load('./../Data/Gandal/preprocessed_data.RData')
datExpr = datExpr %>% data.frame
mean_expr = data.frame('ID'=rownames(datExpr), 'meanExpr' = rowMeans(datExpr))

# PCA
pca = dataset %>% t %>% prcomp

plot_data = data.frame('ID'=rownames(dataset), 'PC1'=pca$rotation[,1], 'PC2'=pca$rotation[,2], 
                       'SFARI'=dataset$SFARI, 'MTcor'=dataset$MTcor, 'GS'=dataset$GS) %>%
            mutate(alpha=ifelse(SFARI, 0.7, 0.2)) %>% left_join(mean_expr, by='ID')

p1 = plot_data %>% ggplot(aes(PC1, PC2, color=MTcor)) + geom_point(alpha=0.7) + scale_color_viridis() + 
     theme_minimal() + ggtitle('Genes coloured by Module-Diagnosis correlation') +
     xlab(paste0('PC1 (',round(100*summary(pca)$importance[2,1]),'%)')) +
     ylab(paste0('PC2 (',round(100*summary(pca)$importance[2,2]),'%)')) +
     theme(legend.position='bottom')

p2 = plot_data %>% ggplot(aes(PC1, PC2, color=GS)) + geom_point(alpha=0.5) + scale_color_viridis() + 
     theme_minimal() + ggtitle('Genes coloured by Gene Significance') + theme(legend.position='bottom')

p3 = plot_data %>% ggplot(aes(PC1, PC2, color=SFARI)) + geom_point(aes(alpha=alpha)) +
     theme_minimal() + ggtitle('Genes coloured by SFARI label') + theme(legend.position='bottom')
p3 = ggExtra::ggMarginal(p3, type='density', groupColour=TRUE, size=10)

p4 = plot_data %>% ggplot(aes(PC1, PC2, color=meanExpr)) + geom_point(alpha=0.5) + scale_color_viridis() + 
     theme_minimal() + ggtitle('Genes coloured by mean level of expression') + theme(legend.position='bottom')

grid.arrange(p1, p2, p3, p4, nrow=2)

rm(pca, datExpr, datGenes, datMeta, dds, DE_info, mean_expr, p1, p2, p3, p4)

Balancing the dataset to obtain a 1:1 ratio in labels

Over-sampling observations with positive SFARI label: Sample with replacement 4x original number of observations

Sample with replacement positive observations in train set

positive_obs = which(train_set$SFARI)

set.seed(123)
add_obs = sample(positive_obs, size=3*length(positive_obs), replace=TRUE)

train_set = train_set[c(1:nrow(train_set), add_obs),]

rm(positive_obs, add_obs)

Under-sampling observations with negative SFARI labels

print(paste0('Keeping ~',round(100*sum(train_set$SFARI)/sum(!train_set$SFARI)),
             '% of the Negative observations in the training set'))

## [1] "Keeping ~19% of the Negative observations in the training set"

negative_obs = which(!train_set$SFARI)
set.seed(123)
remove_obs = sample(negative_obs, size=(sum(!train_set$SFARI)-sum(train_set$SFARI)))

train_set = train_set[-remove_obs,]


rm(negative_obs, remove_obs)

Label distribution in training set

cro(train_set$SFARI)

Labels distribution in test set

cro(test_set$SFARI)

Performance metrics

Confusion matrix

conf_mat = test_set %>% apply_labels(SFARI = 'Actual Labels', 
                                     prob = 'Assigned Probability', 
                                     pred = 'Label Prediction')

cro(conf_mat$SFARI, list(conf_mat$pred, total()))

rm(conf_mat)

Accuracy

acc = mean(test_set$SFARI==test_set$pred)

print(paste0('Accuracy = ', round(acc,4)))

## [1] "Accuracy = 0.6121"

rm(acc)

ROC Curve

pred_ROCR = prediction(test_set$prob, test_set$SFARI)

roc_ROCR = performance(pred_ROCR, measure='tpr', x.measure='fpr')
AUC = performance(pred_ROCR, measure='auc')@y.values[[1]]

plot(roc_ROCR, main=paste0('ROC curve (AUC=',round(AUC,2),')'), col='#009999')
abline(a=0, b=1, col='#666666')

Lift Curve

lift_ROCR = performance(pred_ROCR, measure='lift', x.measure='rpp')
plot(lift_ROCR, main='Lift curve', col='#86b300')

rm(pred_ROCR, roc_ROCR, AUC, lift_ROCR)

Analyse model

SFARI genes have a slightly higher distribution than the rest

plot_data = test_set %>% dplyr::select(prob, SFARI)

plot_data %>% ggplot(aes(prob, fill=SFARI, color=SFARI)) + geom_density(alpha=0.3) + 
              theme_minimal() + ggtitle('Probability distribution by SFARI Label')

• Scores 1 and 2 have the highest scores!

• Score 6 has a completely different behaviour to the rest, with a lower distribution even than the unlabelled genes

plot_data = test_set %>% mutate(ID=rownames(test_set)) %>% dplyr::select(ID, prob) %>%
            left_join(original_dataset %>% mutate(ID=rownames(original_dataset)), by='ID') %>%
            dplyr::select(ID, prob, gene.score) %>% apply_labels(gene.score='SFARI Gene score')

cro(plot_data$gene.score)

mean_vals = plot_data %>% group_by(gene.score) %>% summarise(mean_prob = mean(prob))

plot_data %>% ggplot(aes(prob, color=gene.score, fill=gene.score)) + geom_density(alpha=0.25) + 
              geom_vline(data=mean_vals, aes(xintercept=mean_prob, color=gene.score), linetype='dashed') +
              scale_colour_manual(values=SFARI_colour_hue(r=c(1:6,8,7))) +
              scale_fill_manual(values=SFARI_colour_hue(r=c(1:6,8,7))) + 
              ggtitle('Distribution of probabilities by SFARI score') +
              xlab('Probability') + ylab('Density') + theme_minimal()

ggplotly(plot_data %>% ggplot(aes(gene.score, prob, fill=gene.score)) + geom_boxplot() + 
              scale_fill_manual(values=SFARI_colour_hue(r=c(1:6,8,7))) + 
              ggtitle('Distribution of probabilities by SFARI score') +
              xlab('SFARI score') + ylab('Probability') + theme_minimal())

rm(mean_vals)

summary(fit)

## 
## Call:
## glm(formula = SFARI ~ ., family = "binomial", data = train_set)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.2492  -1.0532   0.0199   1.0436   2.1933  
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  -0.37059    0.05727  -6.471 9.75e-11 ***
## MTcor         0.12633    0.08256   1.530 0.125962    
## GS           -2.76945    1.01602  -2.726 0.006415 ** 
## MM.00C1A8    -0.16808    0.80843  -0.208 0.835303    
## MM.4B9FFF    -2.24179    2.24440  -0.999 0.317873    
## MM.8195FF     0.46242    2.39666   0.193 0.847003    
## MM.C17FFF     8.90924    2.94143   3.029 0.002455 ** 
## MM.C49A00   -11.62208    3.30815  -3.513 0.000443 ***
## MM.D29300    -0.13735    2.28756  -0.060 0.952122    
## MM.FF64B2    -5.58744    1.56680  -3.566 0.000362 ***
## MM.FF699D    -1.71365    0.91484  -1.873 0.061044 .  
## MM.FB61D7    11.05199    2.14017   5.164 2.42e-07 ***
## MM.00C0BB    -4.94969    2.99814  -1.651 0.098755 .  
## MM.53B400     3.76623    3.45902   1.089 0.276236    
## MM.E88523     1.84402    0.68199   2.704 0.006853 ** 
## MM.00B0F6     0.27711    1.21039   0.229 0.818915    
## MM.F365E6    -0.61250    3.31705  -0.185 0.853503    
## MM.FD6F86     8.80736    4.23963   2.077 0.037766 *  
## MM.00BBDD     6.18613    2.22925   2.775 0.005520 ** 
## MM.00B70C    -5.21552    2.99197  -1.743 0.081303 .  
## MM.75AF00    -0.67852    1.12138  -0.605 0.545129    
## MM.DE8C00     0.95878    0.95129   1.008 0.313516    
## MM.B4A000     1.96372    1.67126   1.175 0.239996    
## MM.F8766D    -1.76638    1.46890  -1.203 0.229161    
## MM.00B6EB     3.21914    1.12566   2.860 0.004239 ** 
## MM.00BF7D     3.25031    1.67267   1.943 0.051993 .  
## MM.D774FD     0.94612    2.02591   0.467 0.640491    
## MM.A3A500    -6.20675    2.00338  -3.098 0.001947 ** 
## MM.F17E4F     3.97799    3.19984   1.243 0.213800    
## MM.00C094     5.37684    1.56804   3.429 0.000606 ***
## MM.00A8FF    -3.29108    2.90941  -1.131 0.257977    
## MM.00BECD     1.44690    1.91594   0.755 0.450133    
## MM.A58AFF     1.56584    1.62380   0.964 0.334892    
## MM.E76BF3     2.68760    2.92319   0.919 0.357883    
## MM.FF61C5    -0.94481    1.46724  -0.644 0.519618    
## MM.00BB45    -7.62739    2.58661  -2.949 0.003190 ** 
## MM.8EAB00    -5.44687    1.88788  -2.885 0.003912 ** 
## absGS         0.28926    0.15747   1.837 0.066219 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 7352.9  on 5303  degrees of freedom
## Residual deviance: 6614.0  on 5266  degrees of freedom
## AIC: 6690
## 
## Number of Fisher Scoring iterations: 4

There doesn’t seem to be a relation between the modules’ coefficient and their correlation with Diagnosis, although there is correlation between the variables, so it’s not correct to analyse their coefficients when this happens

Also, this results changes a lot between different runs

var_fit_info = summary(fit)$coefficients %>% as.data.frame %>% 
               mutate(signif=`Pr(>|z|)`<0.05, ID=rownames(summary(fit)$coefficients))

plot_data = original_dataset %>% dplyr::select(matches(clustering_selected), MTcor) 
colnames(plot_data) = c('ID','MTcor')

plot_data = plot_data %>% mutate(ID=gsub('#','MM.',ID)) %>% group_by(ID, MTcor) %>% 
            tally %>% inner_join(var_fit_info, by='ID')

ggplotly(plot_data %>% ggplot(aes(Estimate, MTcor, color=signif, size=n)) + geom_point(aes(id=ID)) + 
         geom_smooth(method='lm', se=FALSE) + theme_minimal() +
         xlab('Coefficient in regression') + ylab('Module-Diagnosis correlation'))

rm(var_fit_info)

Strong correlations between variables

cors = cor(train_set[,-ncol(train_set)])
heatmap.2(cors, dendrogram='none', col=brewer.pal(11,'RdBu'), scale='none', trace='none')

rm(cors)

Print genes with highest scores in test set

• First gene has score=1

• Not a single gene with score 6

test_set %>% dplyr::select(prob, SFARI) %>% mutate(ID = rownames(test_set)) %>% 
             arrange(desc(prob)) %>% top_n(50, wt=prob) %>%
             left_join(original_dataset %>% mutate(ID=rownames(original_dataset)), by='ID')  %>% 
             dplyr::select(ID, prob, SFARI, gene.score, MTcor, matches(clustering_selected)) %>%
             kable

Negative samples distribution

Running the model on all non-SFARI genes

negative_set = dataset %>% filter(!SFARI) %>% dplyr::select(-SFARI)
rownames(negative_set) = rownames(dataset)[!dataset$SFARI]

negative_set$prob = predict(fit, newdata=negative_set, type='response')
negative_set$pred = negative_set$prob>0.5

negative_set = negative_set %>% apply_labels(prob = 'Assigned Probability', 
                                             pred = 'Label Prediction')

cro(negative_set$pred)

cat(paste0('\n', sum(negative_set$pred), ' genes are predicted as ASD-related'))

## 
## 4975 genes are predicted as ASD-related

negative_set %>% ggplot(aes(prob)) + geom_density(color='#F8766D', fill='#F8766D', alpha=0.5) +
                 geom_vline(xintercept=0.5, color='#666666', linetype='dashed') + 
                 ggtitle('Probability distribution of all the Negative samples in the dataset') + 
                 theme_minimal()

negative_set %>% ggplot(aes(prob, GS, color=MTcor)) + geom_point() + geom_smooth(method='loess', color='#666666') +
                 geom_hline(yintercept=0, color='gray', linetype='dashed') +
                 scale_color_gradientn(colours=c('#F8766D','white','#00BFC4')) + 
                 ggtitle('Relation between Probability and Gene Significance') + theme_minimal()

negative_set %>% ggplot(aes(prob, abs(GS), color=MTcor)) + geom_point() + geom_smooth(method='loess', color='#666666') +
                 scale_color_gradientn(colours=c('#F8766D','white','#00BFC4')) + 
                 ggtitle('Relation between Model probability and Gene Significance') + theme_minimal()

negative_set %>% ggplot(aes(MTcor, prob, color=GS)) + geom_point() + geom_smooth(method='loess', color='#666666') + 
                 scale_color_gradientn(colours=c('#F8766D','#F8766D','white','#00BFC4','#00BFC4')) + 
                 xlab('Modules ordered by their correlation to ASD') + ylab('Model probability') +
                 theme_minimal()

plot_data = negative_set %>% group_by(MTcor) %>% summarise(mean = mean(prob), sd = sd(prob), n = n()) %>%
            mutate(MTcor_sign = ifelse(MTcor>0, 'Positive', 'Negative')) %>% left_join(original_dataset, by='MTcor') %>%
            dplyr::select(matches(clustering_selected), MTcor, MTcor_sign, mean, sd, n) %>% distinct()
colnames(plot_data)[1] = 'ID'

ggplotly(plot_data %>% ggplot(aes(MTcor, mean, size=n, color=MTcor_sign)) + geom_point(aes(id=ID)) + 
         geom_smooth(method='loess', color='gray', se=FALSE) + geom_smooth(method='lm', se=FALSE) + 
         xlab('Module-Diagnosis correlation') + ylab('Mean Probability by Model') + theme_minimal())

# Gandal dataset
load('./../Data/Gandal/preprocessed_data_non_standardised_data.RData')
datExpr = datExpr %>% data.frame
DE_info = DE_info %>% data.frame

mean_and_sd = data.frame(ID=rownames(datExpr), meanExpr=rowMeans(datExpr), sdExpr=apply(datExpr,1,sd))

plot_data = negative_set %>% mutate(ID=rownames(negative_set)) %>% left_join(mean_and_sd, by='ID') %>% 
            left_join(original_dataset %>% mutate(ID=rownames(original_dataset)) %>% 
                      dplyr::select(ID, matches(clustering_selected)), by='ID')
colnames(plot_data)[ncol(plot_data)] = 'Module'

plot_data %>% ggplot(aes(meanExpr, prob)) + geom_point(alpha=0.1, color='#0099cc') + 
              geom_smooth(method='loess', color='gray', alpha=0.3) + 
              geom_smooth(method='lm', color='#999999', se=FALSE, alpha=1) + 
              theme_minimal() + ggtitle('Mean expression vs model probability by gene')

rm(mean_and_sd)

plot_data2 = plot_data %>% group_by(Module) %>% summarise(meanExpr = mean(meanExpr), meanProb = mean(prob), n=n())

ggplotly(plot_data2 %>% ggplot(aes(meanExpr, meanProb, size=n)) + geom_point(color=plot_data2$Module) + 
         geom_smooth(method='loess', se=TRUE, color='gray', alpha=0.1, size=0.7) + theme_minimal() + theme(legend.position='none') + 
         ggtitle('Mean expression vs model probability by Module'))

rm(plot_data2)

plot_data %>% filter(sdExpr<0.5) %>% ggplot(aes(sdExpr, prob)) + geom_point(alpha=0.1, color='#0099cc') + 
              geom_smooth(method='loess', color='gray', alpha=0.2) + 
              geom_smooth(method='lm', color='#999999', se=FALSE, alpha=1) + 
              theme_minimal() + ggtitle('SD vs model probability by gene')

plot_data %>% ggplot(aes(meanExpr, sdExpr)) + geom_point(alpha=0.1, color='#0099cc') + 
              geom_smooth(method='loess', color='gray', alpha=0.3) + 
              geom_smooth(method='lm', color='#999999', se=FALSE, alpha=1) + 
              scale_x_log10() + scale_y_log10() +
              theme_minimal() + ggtitle('Mean expression vs SD by gene')

plot_data = negative_set %>% mutate(ID=rownames(negative_set)) %>% 
            left_join(DE_info %>% mutate(ID=rownames(DE_info)), by='ID')

plot_data %>% filter(abs(log2FoldChange)<10) %>%
              ggplot(aes(log2FoldChange, prob)) + geom_point(alpha=0.1, color='#0099cc') + 
              geom_smooth(method='loess', color='gray', alpha=0.3) + 
              theme_minimal() + ggtitle('lfc vs model probability by gene')

Conclusion

Original conclusion: The model is capturing the mean level of expression of the genes (indirectly through module memberhsip), which is a strong bias found in the SFARI scores, but it seems to be capturing a bit of true biological signal as well (based on the GS and the log fold change plots) …

New conclusion: The model seems to be capturing some sort of confounding variable to make the predictions, it would seem that it’s related to the mean expression or the standard deviation of the genes, but in 10_10_20_data_preprocessing_standardising_expr.RData we standardised the dataset and it made no difference in the resulting clusterings, which means that there is some other behaviour related to the level of expression of a gene or its standard deviation that is biasing the classifier, but I don’t know what it could be or how to fix it …

sessionInfo()

## R version 3.5.2 (2018-12-20)
## Platform: x86_64-redhat-linux-gnu (64-bit)
## Running under: Scientific Linux 7.6 (Nitrogen)
## 
## Matrix products: default
## BLAS/LAPACK: /usr/lib64/R/lib/libRblas.so
## 
## locale:
##  [1] LC_CTYPE=en_GB.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_GB.UTF-8        LC_COLLATE=en_GB.UTF-8    
##  [5] LC_MONETARY=en_GB.UTF-8    LC_MESSAGES=en_GB.UTF-8   
##  [7] LC_PAPER=en_GB.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C       
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] expss_0.9.1        ROCR_1.0-7         gplots_3.0.1      
##  [4] Rtsne_0.15         RColorBrewer_1.1-2 gridExtra_2.3     
##  [7] viridis_0.5.1      viridisLite_0.3.0  plotly_4.8.0      
## [10] knitr_1.22         forcats_0.3.0      stringr_1.4.0     
## [13] dplyr_0.8.0.1      purrr_0.3.1        readr_1.3.1       
## [16] tidyr_0.8.3        tibble_2.1.1       ggplot2_3.1.0     
## [19] tidyverse_1.2.1   
## 
## loaded via a namespace (and not attached):
##   [1] colorspace_1.4-1            htmlTable_1.11.2           
##   [3] XVector_0.22.0              GenomicRanges_1.34.0       
##   [5] base64enc_0.1-3             rstudioapi_0.7             
##   [7] bit64_0.9-7                 AnnotationDbi_1.44.0       
##   [9] lubridate_1.7.4             xml2_1.2.0                 
##  [11] splines_3.5.2               geneplotter_1.60.0         
##  [13] Formula_1.2-3               jsonlite_1.6               
##  [15] Cairo_1.5-9                 annotate_1.60.1            
##  [17] broom_0.5.1                 cluster_2.0.7-1            
##  [19] shiny_1.2.0                 compiler_3.5.2             
##  [21] httr_1.4.0                  backports_1.1.2            
##  [23] assertthat_0.2.1            Matrix_1.2-15              
##  [25] lazyeval_0.2.2              cli_1.1.0                  
##  [27] later_0.8.0                 acepack_1.4.1              
##  [29] htmltools_0.3.6             tools_3.5.2                
##  [31] gtable_0.2.0                glue_1.3.1                 
##  [33] GenomeInfoDbData_1.2.0      Rcpp_1.0.1                 
##  [35] Biobase_2.42.0              cellranger_1.1.0           
##  [37] gdata_2.18.0                nlme_3.1-137               
##  [39] crosstalk_1.0.0             xfun_0.5                   
##  [41] rvest_0.3.2                 miniUI_0.1.1.1             
##  [43] mime_0.6                    gtools_3.5.0               
##  [45] XML_3.98-1.11               zlibbioc_1.28.0            
##  [47] scales_1.0.0                hms_0.4.2                  
##  [49] promises_1.0.1              parallel_3.5.2             
##  [51] SummarizedExperiment_1.12.0 yaml_2.2.0                 
##  [53] memoise_1.1.0               rpart_4.1-13               
##  [55] ggExtra_0.8                 RSQLite_2.1.1              
##  [57] latticeExtra_0.6-28         stringi_1.4.3              
##  [59] genefilter_1.64.0           highr_0.8                  
##  [61] S4Vectors_0.20.1            checkmate_1.8.5            
##  [63] caTools_1.17.1              BiocGenerics_0.28.0        
##  [65] BiocParallel_1.16.6         GenomeInfoDb_1.18.2        
##  [67] rlang_0.3.2                 pkgconfig_2.0.2            
##  [69] matrixStats_0.54.0          bitops_1.0-6               
##  [71] evaluate_0.13               lattice_0.20-38            
##  [73] htmlwidgets_1.3             labeling_0.3               
##  [75] bit_1.1-14                  tidyselect_0.2.5           
##  [77] plyr_1.8.4                  magrittr_1.5               
##  [79] DESeq2_1.22.2               R6_2.4.0                   
##  [81] IRanges_2.16.0              generics_0.0.2             
##  [83] Hmisc_4.1-1                 DBI_1.0.0                  
##  [85] DelayedArray_0.8.0          pillar_1.3.1               
##  [87] haven_1.1.1                 foreign_0.8-71             
##  [89] withr_2.1.2                 survival_2.43-3            
##  [91] RCurl_1.95-4.10             nnet_7.3-12                
##  [93] modelr_0.1.4                crayon_1.3.4               
##  [95] KernSmooth_2.23-15          rmarkdown_1.12             
##  [97] locfit_1.5-9.1              grid_3.5.2                 
##  [99] readxl_1.1.0                data.table_1.12.0          
## [101] blob_1.1.1                  digest_0.6.18              
## [103] xtable_1.8-3                httpuv_1.5.0               
## [105] stats4_3.5.2                munsell_0.5.0